Finite Group Databasebeta

← #15834058

Subgroups — #15834058

Order 3328.

592 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13124908C211yesmaximal, characteristic
2#13123853C211yesmaximal, characteristic
3#13123779C211yesmaximal, characteristic, complemented
4#13113737C211yesmaximal, characteristic, complemented
5#13113725C211yesmaximal, characteristic, complemented
6#13113713C211yesmaximal, characteristic, complemented
7#13113706C211yesmaximal, characteristic, complemented
8#13113685C211yesmaximal, characteristic, complemented
9#13113678C211yesmaximal, characteristic, complemented
10#13113654C211yesmaximal, characteristic, complemented
11#13113642C211yesmaximal, characteristic, complemented
12#13113308C211yesmaximal, characteristic, complemented
13#13113221C211yesmaximal, characteristic
14#13113131C211yesmaximal, characteristic, complemented
15C13×#1573C211yesmaximal, characteristic, complemented
16C4×#6127C2211yescharacteristic
17#11719175C2211yescharacteristic
18C13×#432C2211yescharacteristic
19C13×#431C2211yescharacteristic
20C2×C13×C4⋊C8C2211yescharacteristic
21#11718763—21no—
22#11718762—21no—
23#11718586C2211yescharacteristic
24C4×#6099C2211yescharacteristic
25#11718512C411yescharacteristic
26#11718510C411yescharacteristic
27#11718507C411yescharacteristic
28#11718502C411yescharacteristic
29#11718499C2211yescharacteristic
30#11718499C2211yescharacteristic
31#11718492C2211yescharacteristic
32#11718492C2211yescharacteristic
33#11718491C2211yescharacteristic
34#11718491C2211yescharacteristic
35#11718491C2211yescharacteristic
36#11718491C2211yescharacteristic
37#11718489—21no—
38#11718489—21no—
39#11718394C411yescharacteristic
40#11718394C411yescharacteristic
41#11718390—21no—
42#11718390—21no—
43#11718384C411yescharacteristic
44#11718384C411yescharacteristic
45#11718368—21no—
46#11718366—21no—
47C4×Dic52C2211yescharacteristic
48C4×Dic52C2211yescharacteristic
49C4×#6095C2211yescharacteristic
50C4×#6095C2211yescharacteristic
51C13×#335C2211yescharacteristic
52C13×#335C2211yescharacteristic
53C13×#334C2211yescharacteristic
54C13×#334C2211yescharacteristic
55#11718076C2211yescharacteristic
56#11718076C2211yescharacteristic
57#11718076C2211yescharacteristic
58#11718076C2211yescharacteristic
59#11718076C2211yescharacteristic
60#11718076C2211yescharacteristic
61#11718075C2211yescharacteristic
62#11718075C2211yescharacteristic
63#11718047C2211yescharacteristic
64#11718046C2211yescharacteristic
65#11718046C2211yescharacteristic
66C8×#1055C2211yescharacteristic
67C2×#6127C2×C411yescharacteristic
68C22×C8×C13—21no—
69C2×C42×C13C2311yescharacteristic
70C4×C22⋊D13—21no—
71C4×C22⋊D13—21no—
72#88180—21no—
73#88180C2×C411yescharacteristic
74#88178—21no—
75#88178C2×C411yescharacteristic
76#88178C2×C411yescharacteristic
77C2×#6099D411yescharacteristic
78C2×#6099D411yescharacteristic
79C2×Dic52C2×C411yescharacteristic
80C2×Dic52C2×C411yescharacteristic
81C2×#6095C2×C411yescharacteristic
82C2×#6095C2×C411yescharacteristic
83C2×#6094—21no—
84C2×#6094—21no—
85C4×D52C2×C411yescharacteristic
86C4×D52C2311yescharacteristic
87#88126—21no—
88C42×D13—21no—
89#88124—21no—
90#88123C2×C411yescharacteristic
91#88123C2×C411yescharacteristic
92C4×Dic26—21no—
93C4×Dic26C2×C411yescharacteristic
94C4×Dic26C2311yescharacteristic
95C4×Dic26C2311yescharacteristic
96C4×Dic26C2311yescharacteristic
97C13×C4⋊C8—21no—
98C13×C4⋊C8C2×C411yescharacteristic
99C13×C4⋊C8C2×C411yescharacteristic
100C13×C4⋊C8C2311yescharacteristic
101C13×C4⋊C8C2311yescharacteristic
102C13×C4⋊C8C2311yescharacteristic
103C13×C4⋊C8C2311yescharacteristic
104C13×C22⋊C8—21no—
105C13×C22⋊C8C2×C411yescharacteristic
106C13×C22⋊C8C2×C411yescharacteristic
107C13×#97—21no—
108C4×C8×C13C2311yescharacteristic
109C4×C8×C13C2311yescharacteristic
110C22⋊#1055—21no—
111#88061C2×C411yescharacteristic
112#88061C2×C411yescharacteristic
113#88060—21no—
114#88060—21no—
115#88058C2×C411yescharacteristic
116#88058C2×C411yescharacteristic
117#88057C2×C411yescharacteristic
118#88057C2×C411yescharacteristic
119#88056C2×C411yescharacteristic
120#88056C2×C411yescharacteristic
121#88056C2×C411yescharacteristic
122#88056C2×C411yescharacteristic
123#88056C2×C411yescharacteristic
124#88056C2×C411yescharacteristic
125#88055—21no—
126#88055—21no—
127#88054—21no—
128#88054—21no—
129#88054—21no—
130#88054—21no—
131#88054—21no—
132#88054—21no—
133C8×Dic13—21no—
134C8×Dic13—21no—
135C8×Dic13—21no—
136C8×Dic13—21no—
137C4⋊#1055—21no—
138#88043D411yescharacteristic
139#88043D411yescharacteristic
140C4×#1055C2311yescharacteristic
141C4×#1055C2311yescharacteristic
142C4×#1055C2311yescharacteristic
143C4×#1055C2311yescharacteristic
144#18013—131nomaximal, Sylow
145C22×C4×C13C22×C411yescharacteristic
146C22×C4×C13C2×D411yescharacteristic
147C22×C4×C13#4111yescharacteristic
148C2×C22⋊D13—21no—
149#6127—22no—
150#6127—41no—
151C2×D52C22×C411yescharacteristic
152C2×C4×D13—21no—
153C2×C4×D13—21no—
154C2×C4×D13—21no—
155C2×Dic26—21no—
156C2×Dic26C22×C411yescharacteristic
157C2×Dic26C22×C411yescharacteristic
158C2×Dic26C22×C411yescharacteristic
159C2×C8×C13—21no—
160C2×C8×C13—21no—
161C2×C8×C13—21no—
162C2×C8×C13—21no—
163C2×C8×C13—42no—
164C2×C8×C13C22×C411yescharacteristic
165C2×C8×C13C22×C411yescharacteristic
166C2×C8×C13C22×C411yescharacteristic
167C2×C8×C13C22×C411yescharacteristic
168C42×C13C22×C411yescharacteristic
169C42×C13C2×D411yescharacteristic
170C42×C13#4111yescharacteristic
171C42×C13C2411yescharacteristic
172C22⋊Dic13—21no—
173C22⋊Dic13—21no—
174C22⋊Dic13—21no—
175#6103—21no—
176#6103—21no—
177C4⋊Dic13—21no—
178C4⋊Dic13—21no—
179C4⋊Dic13—21no—
180C4⋊Dic13C22×C411yescharacteristic
181C4⋊Dic13C22×C411yescharacteristic
182C4⋊Dic13C22×C411yescharacteristic
183C4⋊Dic13C22×C411yescharacteristic
184#6101—21no—
185#6101—21no—
186#6101—21no—
187#6101—21no—
188#6101—21no—
189#6101—21no—
190C4×Dic13—21no—
191C4×Dic13—21no—
192C4×Dic13—21no—
193C4×Dic13—21no—
194C4×Dic13—21no—
195#6099—22no—
196#6099—41no—
197C2×#1055—21no—
198C2×#1055—21no—
199C2×#1055C2×D411yescharacteristic
200C2×#1055C2×D411yescharacteristic
201C2×#1055C2×D411yescharacteristic
202C2×#1055C2×D411yescharacteristic
203Dic52—22no—
204Dic52—22no—
205#6095—41no—
206#6095—41no—
207#6094—42no—
208#6094—42no—
209#3107—131no—
210#2971—131no—
211#2962—131no—
212#1592—131no—
213#1590—131no—
214#1588—131no—
215#1587—131no—
216#1584—131no—
217#1583—131no—
218#1579—131no—
219C8×Q16—131no—
220#1573D1311yescharacteristic, complemented
221#1497—131no—
222#1477—131no—
223#1453—131no—
224C23×C13C4×D411yescharacteristic
225C22×D13—21no—
226C2×C4×C13—21no—
227C2×C4×C13—21no—
228C2×C4×C13—21no—
229C2×C4×C13—21no—
230C2×C4×C13—41no—
231C2×C4×C13C4×D411yescharacteristic
232C2×C4×C13C4×D411yescharacteristic
233C2×C4×C13C4×D411yescharacteristic
234C2×C4×C13C23×C411yescharacteristic
235C2×C4×C13C22×D411yescharacteristic
236C2×C4×C13C2×#4111yescharacteristic
237C22⋊D13—42no—
238C2×Dic13—21no—
239C2×Dic13—21no—
240C2×Dic13—21no—
241C2×Dic13—21no—
242C2×Dic13—21no—
243C2×Dic13—21no—
244C2×Dic13—21no—
245D52—21no—
246D52—21no—
247C4×D13—42no—
248C4×D13—41no—
249C4×D13—41no—
250C4×D13—81no—
251Dic26—21no—
252Dic26—21no—
253Dic26—21no—
254Dic26—21no—
255Dic26—21no—
256Dic26—81no—
257Dic26#13112yes—
258C8×C13—21no—
259C8×C13—21no—
260C8×C13—21no—
261C8×C13—21no—
262C8×C13—41no—
263C8×C13—41no—
264C8×C13—41no—
265C8×C13—41no—
266#1055—21no—
267#1055—21no—
268#1055—21no—
269#1055—41no—
270#1055—41no—
271#1055#13712yes—
272#533—131no—
273C4×#41—131no—
274#485—131no—
275#485—131no—
276#475—131no—
277#474—131no—
278#462—131no—
279#461—131no—
280#452—131no—
281#452—131no—
282#446—131no—
283#446—131no—
284#446—261no—
285#446—261no—
286C8×Q8—131no—
287C8×Q8—131no—
288C8×Q8—131no—
289C8×Q8—131no—
290C4×Q16—131no—
291C4×Q16—131no—
292C4×SD16—131no—
293C4×SD16—131no—
294#436—131no—
295#436—131no—
296#436—261no—
297#436—261no—
298#432—261no—
299#432C2×D1311yescharacteristic
300#431—131no—
301#431C2×D1311yescharacteristic
302#424—261no—
303C2×C4⋊C8C2×D1311yescharacteristic
304#405—261no—
305C4×M16—131no—
306C4×M16—261no—
307#335C2×D1311yescharacteristic
308#335C2×D1311yescharacteristic
309#334C2×D1311yescharacteristic
310#334C2×D1311yescharacteristic
311Q8⋊C8—131no—
312Q8⋊C8—131no—
313Q8⋊C8—131no—
314Q8⋊C8—131no—
315Q8⋊C8—131no—
316Q8⋊C8—131no—
317D4⋊C8—131no—
318D4⋊C8—131no—
319#322—131no—
320#322—131no—
321#322—131no—
322C82—131no—
323C22×C13—21no—
324C22×C13—21no—
325C22×C13—21no—
326C22×C13C2×C4×D411yescharacteristic
327C2×D13—41no—
328C2×D13—41no—
329C2×D13—41no—
330C4×C13—21no—
331C4×C13—21no—
332C4×C13—21no—
333C4×C13—21no—
334C4×C13C2×#13111yescharacteristic
335C4×C13#56811yescharacteristic
336C4×C13C2×#13711yescharacteristic
337C4×C13#57511yescharacteristic
338Dic13—22no—
339Dic13—41no—
340Dic13—41no—
341Dic13—41no—
342Dic13—41no—
343Dic13—41no—
344Dic13—41no—
345C2×#41—131no—
346C2×Q16—131no—
347C2×Q16—131no—
348C2×SD16—131no—
349C2×SD16—131no—
350C2×M16—131no—
351C2×M16—131no—
352C2×M16—261no—
353C2×M16—261no—
354C22×C8—21no—
355C4⋊Q8—131no—
356C4⋊Q8—131no—
357#125—261no—
358C22⋊Q8—131no—
359C22⋊Q8—131no—
360C22⋊Q8—261no—
361C4×Q8—131no—
362C4×Q8—131no—
363C4×Q8—131no—
364C4×Q8—131no—
365C4×Q8—261no—
366C4×D4—131no—
367C4×D4—131no—
368C4×D4—261no—
369C4×D4—261no—
370#117—131no—
371#117—261no—
372#117—261no—
373C2×C42—261no—
374C2×C42C22×D1311yescharacteristic
375#107—131no—
376#107—131no—
377#106—131no—
378#106—131no—
379C4⋊C8—21no—
380C4⋊C8—261no—
381C4⋊C8—261no—
382C4⋊C8—261no—
383C4⋊C8—261no—
384C4⋊C8—261no—
385C4⋊C8—261no—
386C4⋊C8—261no—
387C4⋊C8C4×D1311yescharacteristic
388C4⋊C8C4×D1311yescharacteristic
389C4⋊C8C22×D1311yescharacteristic
390C4⋊C8C22×D1311yescharacteristic
391C4⋊C8C22×D1311yescharacteristic
392C4⋊C8C22×D1311yescharacteristic
393#103—131no—
394#103—131no—
395#103—131no—
396#103—131no—
397#103—131no—
398#103—131no—
399#102—131no—
400#102—131no—
401C22⋊C8—21no—
402C22⋊C8—261no—
403C22⋊C8—261no—
404C22⋊C8—261no—
405C22⋊C8C4×D1311yescharacteristic
406C22⋊C8C4×D1311yescharacteristic
407#97—21no—
408#97—131no—
409#97—131no—
410#97—261no—
411#97—261no—
412C4×C8—131no—
413C4×C8—131no—
414C4×C8—131no—
415C4×C8—131no—
416C4×C8—261no—
417C4×C8—261no—
418C4×C8—261no—
419C4×C8—261no—
420C4×C8C22×D1311yescharacteristic
421C4×C8C22×D1311yescharacteristic
422C2×C13—41no—
423C2×C13#293311yescharacteristic
424C2×C13C4×#13711yescharacteristic
425C2×C13#295711yescharacteristic
426D13—81no—
427#41—262no—
428#41—521no—
429C2×Q8—131no—
430C2×Q8—131no—
431C2×Q8—131no—
432C2×Q8—261no—
433C2×D4—131no—
434C2×D4—261no—
435C22×C4—261no—
436C22×C4—261no—
437C22×C4—261no—
438C22×C4C2×C4×D1311yescharacteristic
439C22×C4D4×D1311yescharacteristic
440C22×C4#613111yescharacteristic
441Q16—262no—
442Q16—262no—
443SD16—521no—
444SD16—521no—
445M16—262no—
446M16—522no—
447M16—522no—
448M16—521no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—42no—
454C2×C8—131no—
455C2×C8—131no—
456C2×C8—131no—
457C2×C8—131no—
458C2×C8—261no—
459C2×C8—261no—
460C2×C8C2×C4×D1311yescharacteristic
461C2×C8C2×C4×D1311yescharacteristic
462C2×C8C2×C4×D1311yescharacteristic
463C2×C8C2×C4×D1311yescharacteristic
464C4⋊C4—131no—
465C4⋊C4—131no—
466C4⋊C4—131no—
467C4⋊C4—131no—
468C4⋊C4—261no—
469C4⋊C4—261no—
470C4⋊C4—261no—
471C4⋊C4—261no—
472C4⋊C4—261no—
473C4⋊C4—261no—
474C4⋊C4—261no—
475C4⋊C4—261no—
476C4⋊C4—261no—
477C22⋊C4—261no—
478C22⋊C4—261no—
479C22⋊C4—261no—
480C22⋊C4—261no—
481C22⋊C4—261no—
482C42—261no—
483C42—261no—
484C42—261no—
485C42—261no—
486C42—261no—
487C42C2×C4×D1311yescharacteristic
488C42D4×D1311yescharacteristic
489C42#613111yescharacteristic
490C42C23×D1311yescharacteristic
491C13#1801311yescharacteristic, complemented, Sylow
492C23—261no—
493C23#8814711yescharacteristic
494Q8—132no—
495Q8—261no—
496Q8—261no—
497Q8—261no—
498Q8—261no—
499Q8—261no—
500Q8—1041no—
501D4—261no—
502D4—261no—
503D4—522no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—41no—
509C2×C4—261no—
510C2×C4—261no—
511C2×C4—261no—
512C2×C4—261no—
513C2×C4—261no—
514C2×C4—261no—
515C2×C4—261no—
516C2×C4—522no—
517C2×C4—521no—
518C2×C4—521no—
519C2×C4—1041no—
520C2×C4#8814711yescharacteristic
521C2×C4#8814711yescharacteristic
522C2×C4#8814711yescharacteristic
523C2×C4C22×C4×D1311yescharacteristic
524C2×C4C2×D4×D1311yescharacteristic
525C2×C4C2×#613111yescharacteristic
526C8—21no—
527C8—21no—
528C8—21no—
529C8—21no—
530C8—41no—
531C8—41no—
532C8—41no—
533C8—41no—
534C8—132no—
535C8—261no—
536C8—261no—
537C8—261no—
538C8—521no—
539C8—521no—
540C22—21no—
541C22—21no—
542C22—21no—
543C22—521no—
544C22—521no—
545C22—521no—
546C22C2×#8814711yescharacteristic
547C4—21no—
548C4—21no—
549C4—21no—
550C4—21no—
551C4—262no—
552C4—521no—
553C4—521no—
554C4—521no—
555C4—521no—
556C4—521no—
557C4—521no—
558C4D13×#13111yescharacteristic
559C4#1171945511yescharacteristic
560C4#1171947811yescharacteristic
561C4D13×#13711yescharacteristic
562C2—41no—
563C2—1041no—
564C2#1312356011yescharacteristic
565C2#1312365411yescharacteristic
566C2#1312375211yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC13×#1573C2
socleC22×C13C2×C4×D4
prime radicalC2×#6127C2×C4
cosocleC42×C13C24
hypercenter#1573D13
hypocenterC13#18013
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1573

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
3. #13123779C2semidirect
4. #13113737C2semidirect
5. #13113725C2semidirect
6. #13113713C2semidirect
7. #13113706C2semidirect
8. #13113685C2semidirect
9. #13113678C2semidirect
10. #13113654C2semidirect
11. #13113642C2semidirect
12. #13113308C2semidirect
14. #13113131C2semidirect
15. C13×#1573C2semidirect
220. #1573D13semidirect
491. C13#18013semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#131249082
#131238532
#131237792
#131137372
#131137252
#131137132
#131137062
#131136852
#131136782
#131136542
#131136422
#131133082
#131132212
#131131312
C13×#15732
#1801313